pa maurice dirac

Paul Dirac


Paul Adrien Maurice Dirac, OM, FRS (August 8, 1902October 20, 1984) was a British theoretical physicist. Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. He held the Lucasian Chair of Mathematics at the University of Cambridge and spent the last ten years of his life at Florida State University. Among other discoveries, he formulated the Dirac equation, which describes the behavior of fermions and which led to the prediction of the existence of antimatter. Dirac shared the Nobel Prize in physics for 1933 with Erwin Schrödinger, "for the discovery of new productive forms of atomic theory."


Birth and education

Paul Dirac was born in Bristol, England and grew up in the Bishopston area of the city. His father, Charles Dirac, was an immigrant from Saint-Maurice in the Canton of Valais, Switzerland. His mother was originally from Cornwall and the daughter of a mariner. Paul had an elder brother, Félix, who committed suicide in March 1925, and a younger sister, Béatrice. His early family life appears to have been unhappy due to his father's unusually strict and authoritarian nature. He was educated first at Bishop Road Primary School and then at Merchant Venturers' Technical College (later Cotham Grammar School), where his father was a French teacher. The school was an institution attached to the University of Bristol, which emphasized scientific subjects and modern languages. This was an unusual arrangement at a time when secondary education in Britain was still dedicated largely to the classics, and something for which Dirac would later express gratitude.

Dirac studied electrical engineering at the University of Bristol, completing his degree in 1921. He then decided that his true calling lay in the mathematical sciences and, after completing a BA in applied mathematics at Bristol in 1923, he received a grant to conduct research at St John's College, Cambridge, where he would remain for most of his career. At Cambridge, Dirac pursued his interests in the theory of general relativity (an interest he gained earlier as a student in Bristol) and in the nascent field of quantum physics, under the supervision of Ralph Fowler.

Middle years

Dirac noticed an analogy between the Poisson brackets of classical mechanics and the recently proposed quantization rules in Werner Heisenberg's matrix formulation of quantum mechanics. This observation allowed Dirac to obtain the quantization rules in a novel and more illuminating manner. For this work, published in 1926, he received a Ph.D. from Cambridge.

In 1928, building on Wolfgang Pauli's work on non-relativistic spin systems, he proposed the Dirac equation as a relativistic equation of motion for the wavefunction of the electron. This work led Dirac to predict the existence of the positron, the electron's antiparticle, which he interpreted in terms of what came to be called the Dirac sea. The positron was observed by Carl Anderson in 1932. Dirac's equation also contributed to explaining the origin of quantum spin as a relativistic phenomenon.

The necessity of electron matter being created and destroyed in Enrico Fermi's 1934 theory of beta decay, however, led to a reinterpretation of Dirac's equation as a "classical" field equation for any point particle of spin ħ/2, itself subject to quantization conditions involving anti-commutators. Thus reinterpreted as a (quantum) field equation, this Dirac field equation is as central to theoretical physics as the Maxwell, Yang-Mills and Einstein field equations. Dirac is regarded as the founder of quantum electrodynamics, being the first to use that term. He also introduced the idea of vacuum polarization in the early 1930s. This work was key to the development of quantum mechanics by the next generation of theorists, and in particular Schwinger, Feynman, Sin-Itiro Tomonaga and Dyson in their formulation of quantum electrodynamics.

Dirac's Principles of Quantum Mechanics, published in 1930, is a landmark in the history of science. It quickly became one of the standard textbooks on the subject and is still used today. In that book, Dirac incorporated the previous work of Werner Heisenberg on matrix mechanics and of Erwin Schrödinger on wave mechanics into a single mathematical formalism that associates measurable quantities to operators acting on the Hilbert space of vectors that describe the state of a physical system. The book also introduced the delta function. Following his 1939 article, he also included the bra-ket notation in the third edition of his book, thereby contributing to its universal use nowadays.

In 1933, following his 1931 paper on magnetic monopoles, Dirac showed that the existence of a single magnetic monopole in the universe would suffice to explain the observed quantization of electrical charge. In 1975 and 1982 intriguing results suggested the possible detection of magnetic monopoles, but there is to date no convincing evidence for their existence.

He married Eugene Wigner's sister, Margit, in 1937. He adopted Margit's two children, Judith and Gabriel. Paul and Margit Dirac had two children together, both daughters, Mary Elizabeth and Florence Monica.

Later years

Dirac was the Lucasian Professor of Mathematics at Cambridge from 1932 to 1969. In 1937, he proposed a speculative cosmological model based on the so called large numbers hypothesis. During World War II, he conducted important theoretical and experimental research on uranium enrichment by gas centrifuge.

Dirac's quantum electrodynamics made predictions that were - more often than not - infinite and therefore unacceptable. A workaround known as renormalization was developed, but Dirac never accepted this. "I must say that I am very dissatisfied with the situation," he said in 1975, "because this so-called 'good theory' does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it is small — not neglecting it just because it is infinitely great and you do not want it! His refusal to accept renormalization, resulted in his work on the subject moving increasingly out of the mainstream. After having relocated to Florida in order to be near his elder daughter, Mary, Dirac spent his last ten years (of both life and physics research) at Florida State University (FSU) in Tallahassee, Florida.

Amongst his many students was John Polkinghorne, who recalls that Dirac "was once asked what was his fundamental belief. He strode to a blackboard and wrote that the laws of nature should be expressed in beautiful equations.

Death and afterwards

In 1984 Dirac died in Tallahassee, Florida where he is buried. The Dirac-Hellmann Award at FSU was endowed by Dr Bruce P. Hellmann (Dirac's last doctoral student) in 1997 to reward outstanding work in theoretical physics by FSU researchers. The Paul A.M. Dirac Science Library at FSU is named in his honor. In 1995, a plaque in his honour bearing his equation was unveiled at Westminster Abbey in London with a speech from Stephen Hawking. A commemorative garden has been established opposite the railway station in Saint-Maurice, Switzerland, the town of origin of his father's family.

Honours and awards

Dirac shared the 1933 Nobel Prize for physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory." Dirac was also awarded the Royal Medal in 1939 and both the Copley Medal and the Max Planck medal in 1952. He was elected a Fellow of the Royal Society in 1930, and of the American Physical Society in 1948.

In 1975 Dirac gave a series of five lectures at the University of New South Wales which were subsequently published as a book, Directions of Physics (Wiley, 1978 – H. Hora and J. Shepanski, eds.). Dirac donated the royalties from this book to the University for the establishment of the Dirac Lecture Series . The Silver Dirac Medal for the Advancement of Theoretical Physics is awarded by the University of New South Wales on the occasion of the Public Dirac Lecture.

Immediately after his death, two organizations of professional physicists established annual awards in Dirac's memory. The Institute of Physics, the United Kingdom's professional body for physicists, awards the Paul Dirac Medal and Prize for "outstanding contributions to theoretical (including mathematical and computational) physics". The first three recipients were Stephen Hawking (1987), John Stewart Bell (1988), and Roger Penrose (1989). The Abdus Salam International Centre for Theoretical Physics (ICTP) awards the Dirac Medal of the ICTP each year on Dirac's birthday (August 8). Also, the Dirac Prize is awarded by the International Centre for Theoretical Physics in his memory.

The street on which the National High Magnetic Field Laboratory in Tallahassee, Florida, is located was named Paul Dirac Drive. There is also a road named after him in his home town of Bristol, UK. The BBC named its video codec Dirac in his honour. And in the popular British television show Doctor Who, the character Adric was named after him (Adric is an anagram of Dirac).


Dirac was known among his colleagues for his precise and taciturn nature. When Niels Bohr complained that he did not know how to finish a sentence in a scientific article he was writing, Dirac replied, "I was taught at school never to start a sentence without knowing the end of it." He criticized the physicist J. Robert Oppenheimer's interest in poetry: "The aim of science is to make difficult things understandable in a simpler way; the aim of poetry is to state simple things in an incomprehensible way. The two are incompatible.

Dirac himself wrote in his diary during his postgraduate years that he concentrated solely on his research, and only stopped on Sunday, when he took long strolls alone.

According to a story told in different versions, a friend or student visited Dirac, not knowing of his marriage. Noticing the visitor's surprise at seeing an attractive woman in the house, Dirac said, "This is... this is Wigner's sister". Margit Dirac told both George Gamow and Anton Z. Capri in the 1960s that her husband had actually said, "Allow me to present Wigner's sister, who is now my wife.

Dirac was also noted for his personal modesty. He called the equation for the time evolution of a quantum-mechanical operator, which he was the first to write down, the "Heisenberg equation of motion". Most physicists speak of Fermi-Dirac statistics for half-integer-spin particles and Bose-Einstein statistics for integer-spin particles. While lecturing later in life, Dirac always insisted on calling the former "Fermi statistics". He referred to the latter as "Einstein statistics" for reasons, he explained, of "symmetry".

Religious views

Dirac once said "God used beautiful mathematics in creating the world". Heisenberg recollects a friendly conversation among young participants at the 1927 Solvay Conference about Einstein and Planck's views on religion. Wolfgang Pauli, Heisenberg and Dirac took part in it. Dirac's contribution was a poignant and clear criticism of the political manipulation of religion, which was much appreciated for its lucidity by Bohr, when Heisenberg reported it to him later. Among other things, Dirac said: "I cannot understand why we idle discussing religion. If we are honest—and as scientists honesty is our precise duty—we cannot help but admit that any religion is a pack of false statements, deprived of any real foundation. The very idea of God is a product of human imagination.... I do not recognize any religious myth, at least because they contradict one another...." Heisenberg's view was tolerant. Pauli had kept silent, after some initial remarks, but when finally he was asked for his opinion, jokingly he said: "Well, I'd say that also our friend Dirac has got a religion and the first commandment of this religion is 'God does not exist and Paul Dirac is his prophet.'" Everybody burst into laughter, including Dirac.


Dirac is widely regarded as one of the greatest physicists of all time. He was one of the founders of quantum mechanics and quantum electrodynamics, and some physicists, among them Antonino Zichichi, consider Dirac the greatest physicist of the 20th century.

His early contributions include the modern operator calculus for quantum mechanics, which he called transformation theory, and an early version of the path integral. He formulated a many-body formalism for quantum mechanics which allowed each particle to have its own proper time.

His relativistic wave equation for the electron was the first successful attack on the problem of relativistic quantum mechanics. Dirac founded quantum field theory with his reinterpretation of the Dirac equation as a many body equation, which predicted the existence of antimatter and matter/antimatter annihilation. He was the first to formulate quantum electrodynamics, although he could not calculate arbitrary quantities because the short distance limit requires renormalization.

In an attempt to solve the quantum divergence problem, Dirac gave a classical point particle theory combining advanced and retarded waves to eliminate the classical electron self-energy. Although these classical methods did not immediately solve the problems in quantum electrodynamics, they did lead John Archibald Wheeler and Richard Feynman to formulate an alternate Green's function description for light, which eventually led to Feynman's point particle formulation of quantum field theory.

Dirac discovered the magnetic monopole solutions, the first topological configuration in physics, and used them to give the modern explanation of charge quantization. He developed constrained quantization in the 1960s, identifying the general quantum rules for arbitrary classical systems.

Dirac's quantum-field analysis of the vibrations of a membrane, in the early 1960s, proved extremely useful to modern practitioners of Superstring theory and its closely related successor, M-Theory.

Selected bibliography

  • Principles of Quantum Mechanics (1930): This book summarizes the ideas of quantum mechanics using the modern formalism that was largely developed by Dirac himself. Towards the end of the book, he also discusses the relativistic theory of the electron (the Dirac equation), which was also pioneered by him. This work does not refer to any other writings then available on quantum mechanics.
  • Lectures on Quantum Mechanics (1966): Much of this book deals with quantum mechanics in curved space-time.
  • General Theory of Relativity (1975): This 68-page work summarizes Einstein's general theory of relativity.

See also



  • The Second Creation: makers of the revolution in twentieth century physics by Robert P. Crease and Charles C. Mann, 1986 Macmillan Publishing, New York, 1996 (revised), Rutgers University Press. Entertaining personality-based history of particle physics/quantum mechanics in the twentieth century.
  • QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan S. Schweber, Princeton University Press, 1994. Includes a chapter on Dirac as the founder of quantum electrodynamics.
  • "Paul Adrien Maurice Dirac"

Dirac videos

External links

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